Loading [MathJax]/jax/output/HTML-CSS/config.js
full
search.png

Search

close.png

Cancel

arrow
Volume 4, Issue 2
A Triangular Spectral Method for the Stokes Equations

Lizhen Chen, Jie Shen & Chuanju Xu

DOI: 10.4208/nmtma.2011.42s.3

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 158-179.

Published online: 2011-04

Preview Full PDF 3460 36059

Cited by

google scholar semantic scholar
Export citation
  • Abstract

A triangular spectral method for the Stokes equations is developed in this paper. The main contributions are two-fold: First of all, a spectral method using the rational approximation is constructed and analyzed for the Stokes equations in a triangular domain. The existence and uniqueness of the solution, together with an error estimate for the velocity, are proved. Secondly, a nodal basis is constructed for the efficient implementation of the method. These new basis functions enjoy the fully tensorial product property as in a tensor-produce domain. The new triangular spectral method makes it easy to treat more complex geometries in the classical spectral-element framework, allowing us to use arbitrary triangular and tetrahedral elements.

  • Keywords

Stokes equations, triangular spectral method, error analysis.

  • AMS Subject Headings

65N35, 65N22, 65F05, 35J05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-4-158, author = {Lizhen Chen, Jie Shen and Chuanju Xu}, title = {A Triangular Spectral Method for the Stokes Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {2}, pages = {158--179}, abstract = {

A triangular spectral method for the Stokes equations is developed in this paper. The main contributions are two-fold: First of all, a spectral method using the rational approximation is constructed and analyzed for the Stokes equations in a triangular domain. The existence and uniqueness of the solution, together with an error estimate for the velocity, are proved. Secondly, a nodal basis is constructed for the efficient implementation of the method. These new basis functions enjoy the fully tensorial product property as in a tensor-produce domain. The new triangular spectral method makes it easy to treat more complex geometries in the classical spectral-element framework, allowing us to use arbitrary triangular and tetrahedral elements.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.42s.3}, url = {http://global-sci.org/intro/article_detail/nmtma/5963.html} }
TY - JOUR T1 - A Triangular Spectral Method for the Stokes Equations AU - Lizhen Chen, Jie Shen & Chuanju Xu JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 158 EP - 179 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.42s.3 UR - https://global-sci.org/intro/article_detail/nmtma/5963.html KW - Stokes equations, triangular spectral method, error analysis. AB -

A triangular spectral method for the Stokes equations is developed in this paper. The main contributions are two-fold: First of all, a spectral method using the rational approximation is constructed and analyzed for the Stokes equations in a triangular domain. The existence and uniqueness of the solution, together with an error estimate for the velocity, are proved. Secondly, a nodal basis is constructed for the efficient implementation of the method. These new basis functions enjoy the fully tensorial product property as in a tensor-produce domain. The new triangular spectral method makes it easy to treat more complex geometries in the classical spectral-element framework, allowing us to use arbitrary triangular and tetrahedral elements.

Lizhen Chen, Jie Shen and Chuanju Xu. (2011). A Triangular Spectral Method for the Stokes Equations. Numerical Mathematics: Theory, Methods and Applications. 4 (2). 158-179. doi:10.4208/nmtma.2011.42s.3
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard